The synthesis of the two currently used superhard materials, diamond and cubic boron nitride, is briefly described with indications of the factors influencing the quality of the crystals obtained. The physics of hardness is discussed and the importance of covalent bonding and fixed atomic positions in the crystal structure, which determine high hardness values, is outlined. The materials investigated to date are described and new potentially superhard materials are presented. No material that is thermodynamically stable under ambient conditions and composed of light (small) atoms will have a hardness greater than that of diamond. Materials with hardness values similar to that of cubic boron nitride (cBN) can be obtained. However, increasing the capabilities of the high-pressure devices could lead to the production of better quality cBN compacts without binders.